What is her normal rowing speed with no wind? (full question in description)

Question

On a particular day, the wind added 3 miles per hour to Jaime's rate when she was rowing with the wind and subtracted 3 miles per hour from her rate on her return trip. Jaime found that in the same amount of time she could row 48 miles with the wind, she could go only 30 miles against the wind.What is her normal rowing speed with no wind?

 

 

Answer 1

D=R*T

Distance = Rate times Time

Distance U for upwind = Rate U * Time U

Distance D for downwind = Rate D * Time D

Distance U = 30

Distance D = 48

Base Rate =  Rate B

Rate U = Rate B - 3

Rate D = Rate B + 3

Therefore; 

DU = (RB-3) * TU

DD = (RB+3) * TD

TD = TU; therefore; DU/(RB-3) = DD/(RB+3); solving this algebraically gives you

DU*RB + DU*3 = DD*RB-DD*3

Subbing in DU and DD gives you

30RB + 90 = 48RB - 144

Move the 48 RB to the left and the 90 to the right gives you

-18RB = -234

Divide both sides by -18 gives you the answer:

RB = 13.

You can check this and verify it is correct.  

 

Good luck!  

Answer 2

Let x = Jaime's rate of rowing with no wind

 

x + 3 = rate with the wind

x - 3 = rate against the wind

 

Distance = (Rate)(Time), so Time = Distance/Rate

 

Time to go 48 miles with wind = Time to go 30 miles against wind

 

So, 48/(x+3) = 30/(x-3)

 

Cross multiply to obtain 48(x-3) = 30(x+3)

 

48x - 144 = 30x + 90

 

18x = 234

 

    x = 13 mph